Geodesic
Goffin's algorithm for zonotopes
Kybernetika, Tome 48 (2012) no. 5, pp. 890-906 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The Löwner-John ellipse of a full-dimensional bounded convex set is a circumscribed ellipse with the property that if we shrink it by the factor $n$ (where $n$ is dimension), we obtain an inscribed ellipse. Goffin's algorithm constructs, in polynomial time, a tight approximation of the Löwner-John ellipse of a polyhedron given by facet description. In this text we adapt the algorithm for zonotopes given by generator descriptions. We show that the adapted version works in time polynomial in the size of the generator description (which may be superpolynomially shorter than the facet description).
The Löwner-John ellipse of a full-dimensional bounded convex set is a circumscribed ellipse with the property that if we shrink it by the factor $n$ (where $n$ is dimension), we obtain an inscribed ellipse. Goffin's algorithm constructs, in polynomial time, a tight approximation of the Löwner-John ellipse of a polyhedron given by facet description. In this text we adapt the algorithm for zonotopes given by generator descriptions. We show that the adapted version works in time polynomial in the size of the generator description (which may be superpolynomially shorter than the facet description).
Classification : 52B12, 52B55, 68U05, 90C57
Keywords: Löwner–John ellipse; zonotope; Goffin's algorithm; ellipsoid method 
@article{KYB_2012_48_5_a4,
     author = {\v{C}ern\'y, Michal},
     title = {Goffin's algorithm for zonotopes},
     journal = {Kybernetika},
     pages = {890--906},
     year = {2012},
     volume = {48},
     number = {5},
     mrnumber = {3086858},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012_48_5_a4/}
}
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Černý, Michal. Goffin's algorithm for zonotopes. Kybernetika, Tome 48 (2012) no. 5, pp. 890-906. http://geodesic.mathdoc.fr/item/KYB_2012_48_5_a4/